Methods for producing three-dimensional (3D) articles by thermally reforming two-dimensional (2D) glass sheets are known from, for example, International Publication Numbers WO2010/002446, WO2010/061238, WO2010/065371, and WO2010/065349, all by Corning Incorporated et al. These methods generally involve loading a 2D glass sheet onto a relatively cold mold, heating the mold and the 2D glass sheet to an elevated temperature at which the glass sheet can be deformed, shaping the 2D glass sheet into a desired 3D article using the mold, cooling the 3D article in the mold, and unloading the 3D article from the mold. These methods have in common a very long residence time of the glass in the mold, i.e., from the time the glass is loaded into the mold to the time the glass is unloaded from the mold. Typical residence times are between 6 minutes and 1 hour. Mass production of 3D articles using these methods would have a low throughput and require a large number of molds.